CASA Function: toProjective

Converts the algebraic set to the corresponding algebraic set in projective space.

Calling Sequence:

• P := toProjective(a)
• P := toProjective(a,x)

Parameters:

a : algset("impl")

• Algebraic set in affine or projective implicit representation.

x : name

• The homogenization variable. This variable must not be in the variable list of a.

Result:

P : algset("impl")

• The corresponding algebraic set in projective space.

Description:

• The function converts an algebraic set in implicit representation to the corresponding algebraic set in implicit form but lying in projective space.
• If the given algebraic set is already in projective space, it is returned immediately.
• If no homogenization variable is provided, a new variable will be chosen that is neither among the variables nor the parameters of a.

Examples:

> a:=mkImplAlgSet([x^2-2*y^3+4*x*y^2],[x,y]);

> b:=toProjective(a);

> c:=toProjective(a,H);

> [isProjective(a),isProjective(b),isProjective(c)];

See Also: